Dresden 2026 – scientific programme

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SOE: Fachverband Physik sozio-ökonomischer Systeme

SOE 15: Networks: From Topology to Dynamics III (joint session DY/SOE)

SOE 15.3: Talk

Thursday, March 12, 2026, 11:45–12:00, ZEU/0118

Linear dynamics on infinite networks — •Bernd Michael Fernengel — HIFMB, Oldenburg, Germany

Linear evolutionary equations are often used to describe the time evolution of a physical system. Their solution operator can be written in an exponential form of exp(t A), with some generator A. When the generator is a finite dimensional matrix, we can interpret its time evolution as a hopping dynamics on a finite network, where the dynamics of the network can be transferred to the dynamics of the solution operator.

In order to study special types of solution operators for non-interacting systems of countable dimensions, we construct countable, infinitely large networks using the iterated Cartesian product of finite graphs, where the dynamics is known. We discuss the possibilities to infer properties like the time evolution and the stationary solution of the infinite network from finite approximations via the thermodynamic limit. This is closely related to the question, under which conditions it is possible to approximate a countable, infinite system by finite subsystems.

Keywords: Countable infinite networks; Cartesian product of graphs; Thermodynamic limit; Non-interacting systems